Westlake Online Math Forum第十五期 | Matteo Ruggiero: Resolution of vector fields and applications to parabolic dynamics

2023-11-14 16:18:23


地点:E4-233 & ZOOM

ZOOM ID:939 5754 1624

PASSCODE: 575859

主讲人: Université Paris Cité Matteo Ruggiero

主讲人介绍: Matteo Ruggiero is maître de conférences at the Université Paris Cité, UFR de Mathématiques, research unit IMJ-PRG, group Géométrie et Dynamique. His interests include (Local and semi-local) dynamics of analytic maps, (non-Kähler) complex geometry and compactification of orbit spaces, birational aspects of singularities of analytic spaces and maps, links with toric, tropical and non-archimedean geometry.

讲座主题:Resolution of vector fields and applications to parabolic dynamics


The local dynamical properties of a high order perturbation of the identity are intimately related to the resolution of singularities of the associated infinitesimal generator.

In particular, Ramis-Sibuya normal forms of resolved infinitesimal generators admitting a separatrix allow to describe the parabolic manifolds asymptotic to such separatrix (by recent works by López-Hernanz, Raissy, Ribón, Sanz-Sánchez, Vivas).

I will present these phenomena via a class of examples in dimension 3, introduced in a joint work with Samuele Mongodi, where all the separatrices lie inside central manifolds of the resolved infinitesimal generator, a behavior in contrast with the situation in dimension 2.